Abstract
Helium that accretes onto a carbon/oxygen white dwarf in double white dwarf AM Canum Venaticorum (AM CVn) binaries undergoes unstable thermonuclear flashes when the orbital period is in the 3.5-25 minute range. At the shortest orbital periods (and highest accretion rates, MË™>10<SUP>-7</SUP> M<SUB>solar</SUB> yr<SUP>-1</SUP>), the flashes are weak and likely lead to the helium equivalent of classical nova outbursts. However, as the orbit widens and MË™ drops, the mass required for the unstable ignition increases, leading to progressively more violent flashes up to a final flash with helium shell mass ~0.02-0.1 M<SUB>solar</SUB>. The high pressures of these last flashes allow the burning to produce the radioactive elements <SUP>48</SUP>Cr, <SUP>52</SUP>Fe, and <SUP> 56</SUP>Ni that power a faint (M<SUB>V</SUB>=-15 to -18) and rapidly rising (few days) thermonuclear supernova. Current galactic AM CVn space densities imply one such explosion every 5,000-15,000 years in 10<SUP>11</SUP> M<SUB>solar</SUB> of old stars (~2%-6% of the Type Ia rate in E/SO galaxies). These ``.Ia'' supernovae (one-tenth as bright for one-tenth the time as a Type Ia supernovae) are excellent targets for deep (e.g., V=24) searches with nightly cadences, potentially yielding an all-sky rate of 1000 per year.
